How is the transfer function determined for a PID controller
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I'm reading a tutorial on PID controller, and the transfer function for a mass-spring damper system is given as follows:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/678738/image.jpeg)
where m = 1 , b = 10, k = 20. If a proportional gain is added to the controller, the new tranfser function becomes:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/678743/image.jpeg)
How is the new transfer function derived?
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